This project supports research to develop new statistical methodology applicable to the biomedical sciences. We developed statistical methods to analyze seasonal and cyclical variation in disease rates, including powerful methods for detecting seasonal patterns and cyclical trends. We developed and assessed methods for analyzing geographic variation in disease rates from small geographic units, such as U.S. counties. We proposed and tested a new measure of the extent of intrinsic geographic variability of these rates, based on a mixed effect model that allows one to separate intrinsic variability from random count variability. Using this model, we also developed estimation procedures that reduced the impact of random variation, and we compared these procedures with other procedures based on various adjusted and unadjusted rates to determine which methods could reliably rank the disease risk among the geographic units, while avoiding the spurious effects of random variation. We developed methods for determining "hot spots" for mutations in a defined DNA sequence, including exact methods to analyze small numbers of experiments evaluating mutations in plasmids as well as large sample methods for evaluating mutations in a gene such as the p53 gene. We improved a computer program to choose the subset of several available foods that leads to the best estimate of the intake of a specific nutrient from answers to a food-frequency questionnaire. We developed sample size calculations to establish the equivalence of two treatments in stratified clinical trials. We also extended the k-ratio Bayes method for comparing multiple factors in an experimental setting. This extension allows for multiple interim tests of the difference between two treatments as data accumulate and permits stopping a trial not only when the treatment difference is significant, but also when the difference is too small to warrant continuing the trial. Finally, we developed methods for examining birth cohort and calendar period trends in disease rates, including improved parametric approaches; a simulation study demonstrated that our recently developed nonparametric methods have good operating characteristics.